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An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays

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Abstract

This paper investigates the problem of exponential synchronization of switched stochastic competitive neural networks (SSCNNs) with both interval time-varying delays and distributed delays. The distributed delays can be unbounded or bounded; the stochastic perturbation is of the form of multi-dimensional Brownian motion, and the networks are governed by switching signals with average dwell time. Based on new multiple Lyapunov-Krasovkii functionals, the free-weighting matrix method, Newton-Leibniz formulation, as well as the invariance principle of stochastic differential equations, two sufficient conditions ensuring the exponential synchronization of drive-response SSCNNs are developed. The provided conditions are expressed in terms of linear matrix inequalities, which are dependent on not only both lower and upper bounds of the interval time-varying delays but also delay kernel of unbounded distributed delays or upper bounds for bounded distributed delays. Control gains and average dwell time restricted by given conditions are designed such that they are applicable in practice. Numerical simulations are given to show the effectiveness of the theoretical results.

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Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China (60874088), the Natural Science Foundation of Jiangsu Province of China (BK2009271), the National Natural Science Foundation of China (10801056), the Foundation of Chinese Society for Electrical Engineering (2008), the Excellent Youth Foundation of Educational Committee of Hunan Provincial (10B002), the Key Project of Chinese Ministry of Education (211118), the Scientific Research Fund of Yunnan Province (2010ZC150).

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Authors and Affiliations

  1. Department of Mathematics, Honghe University, Mengzi, 661100, Yunnan, China

    Xinsong Yang

  2. Department of Mathematics, College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, 410114, Hunan, China

    Chuangxia Huang

  3. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

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  1. Xinsong Yang
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  2. Chuangxia Huang
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  3. Jinde Cao
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Correspondence to Chuangxia Huang.

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Yang, X., Huang, C. & Cao, J. An LMI approach for exponential synchronization of switched stochastic competitive neural networks with mixed delays. Neural Comput & Applic 21, 2033–2047 (2012). https://doi.org/10.1007/s00521-011-0626-2

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  • DOI: https://doi.org/10.1007/s00521-011-0626-2

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